Fair point about problem-fit - some problems do naturally lend themselves to one approach over the other.

But I think the Sudoku example is less about top-down vs bottom-up and more about dogmatic adherence to abstractions (OOP in that case). Jeffries wasn't just using a 'hacker' approach - he was forcing everything through an OOP lens that fundamentally didn't fit the problem structure.

But yes, same issue can happen with the 'mathematical' approach - forcing "elegant" closed-form thinking onto problems that are inherently messy or iterative.

I don’t think his failure had anything to do with OOP. He failed because he deliberately refused to think systematically about the problem before writing code, per the dictates of TDD.

I'd argue that everyone solves problems bottoms up. It's just that some people have done the problem before (or a variant of it) so they have already constructed a top-down schema for it.

No, there's a difference. The difference is whether you work in constraint space (top down) or in solution space (bottom up). Top down is effectively adding constraints until there is a single solution.

The hacker’s mentality is like that of the painter who spends months on a portrait in order to produce a beautiful but imperfect likeness, marked with his own personal style, which few can replicate and people pay a lot for. The mathematical approach is to take a photo because someone figured out how to perfectly reproduce images on paper over a hundred years ago and I just want a picture, dammit, but the camera’s manual is in Lojban.

IMO, the mathematical approach is essentially always better for software; nearly every problem that the industry didn’t inflict upon itself was solved by some egghead last century. But there is a kind of joy in creating pointless difficulties at enormous cost in order to experience the satisfaction of overcoming them without recourse to others, I suppose.